414 



H. M. KYLE 



[DECEMBER 



heading are arranged the frequencies of the variations, under the third 

 the average or standard deviation of the variations for each successive 

 group of five characters, and under the fourth the probable error of 

 each group. 



Average deviation for all the characters l - 29 



Probable error 



1-09. 



The conclusion one would draw from these two examples is that the 

 assumption which permits theory and observation to agree so closely 

 cannot be far from correct. The characters were not taken in any 

 fixed order, and the results show how the observed values fluctuate 

 about the theoretical, the first group having an average deviation 

 lower than the theoretical value, whilst the second and third have higher. 

 This fluctuation gives point to an important corollary founded by Prof. 

 Heincke on the theory shown above, namely, that if one or two char- 

 acters only of all the individuals of a fixed group could be examined 

 the variations would also agree with this law. The difficulty of ob- 

 taining this fixed group of individuals similar in all respects as to age 

 or size, place or living conditions, etc., is therefore the only drawback. 



A second corollary of even greater importance is also deduced 

 from this theory. If this formula represents the " essence " of the 

 variations of all the individuals, the conditions being the same, it must 

 also do so for one. The variations of each individual are equally 

 balanced on either side of the average, that is, if the variations of all 

 the characters of each single individual could be tabulated they would 

 be distributed about the mean according to the above law. 

 1 The signs + and 



are not used in obtaining the " Average deviation." 



